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A Multiscale Prediction of Elasticity of Cement Paste at Early Age Based on Percolation



AbstractAs an evolving component of concrete, the cement paste plays an important role on the mechanical properties. It is well known that the mechanical characteristics of cement paste, which is random, complex, multiscale composite, follows a rapid change at early age. This paper focuses on the evolution in the elasticity of the cement paste during the hydration, e.g. Young’s modulus and Poisson’s ration, which proposed by the homogenization method combined  the percolation algorithm with individual phase intrinsic elasticity. A paste development model of the cement, named CEMHYD3D, is used to capture an accurate microstructural model. The model results are in good agreement with the experimental data and other numerical results, which are available in the open literature.

Keywords:Multiscale; Microstructure; Early age; Cement paste; Percolation; Elasticity



Young’s modulus, in which the compressive and tensile strengthof hardening and hardened cement-based materials are the vital parameters used in the structural design and analysis of concrete structure. Especially, it is known that the rate of development of Yong’s modulus is considerably faster than that of compressive and tensile strength, which is reaching a significant fraction of its final value after a few days. The stresses that are generated in structures are also closely related to the rapid development of the Young’s modulus, which makes it as an essential parameter to be studied in order to better understand the behavior of the cement-based materials. It is very helpful to know the microstructure evolution of the hydrating material to understand the development of  the material properties, as it is believed that, at the microstructure level , the microstructure evolution governs the material mechanical properties[Maekawa  et al., 2009; Breugel, 1991; Garboczi  et al., 1999; Venkiteela  et al., 2010].

Bernard proposed an analytical homogenization approach to study the aging elasticity of cement-based materials[Bernardet al., 2003]. The authors considered the microstructure of the concrete at four different levels, and chose a suitable homogenization approach, e.g. Mori-Tanaka scheme(MT) and/or self-consistent scheme(SCS) at each level, which bridge the gap between the physical and chemistry during the process of hydration and the mechanics, however, the proposed model could only give realistic values for high water to cement(w/c) ratios and fail to predict the low w/c ratios for obtaining non-zero values below percolation threshold. Sanahuja modified the aspect ratio of the hydration product to predict the elasticity of cement-based materials at early age[Sanahujaet al., 2007]. Still, the authors did not successfully predict the evolution of Young’s modulus at the early age, e.g. the hydration degree is smaller than 0.3. Smilauer reconstructed a digital image of the hydrating cement paste given by the CEMHYD3D hydration model[Smilaueret al., 2007;Bentz, 2000]. The authors showed that numerical homogenization yielded more accurate results, however, the presented method is only appropriate for a w/c ratio higher than 0.35 and predict a stiffer response of Young’s modulus at early age, besides, the FEM method was a too heavy computational method for the computation of development of properties of cement paste at early age. Sun proposed a approach that considered hydrate products coming into contact with the advancement of hydration and the contact area among the particles, which was the essential factor that dominates the mechanical properties of the system[Sunet al., 2005]. Sanahuja improved the prediction accuracy of early age elasticity evolution by modifying the aspect ratio of C-S-H and in terms of percolation threshold, and clearly illustrated a change in the response of the homogenization method used by changing the morphology of the inclusion[Sanahujaet al., 2007], which was generally considered sphere-shaped [Pichleret al., 2009].  Still, they pointed out that the agreement was not good at very early age, e.g. hydration degree was smaller than 0.3. Therefore, it is problematic for the prediction of elasticity of cement paste at early age without considering the transition from a suspension to a solid structure.

The goal of this paper is to propose a model relating the intrinsic properties of its individual chemical phase in effective elastic properties of cement paste at the nano- and micro-level using upscaling methods, for the prediction of elasticity of cement paste, especially at very early age when cement-based material evolves from a close to plastic state to a solid state by applying solid phase percolation concept.

2. Fundamentals of continuum micromechanics

2.1. Representative volume elements (RVE) and separation of scales principle

The transition material is from a heterogeneous material to a homogeneous materialat higher level requires statistically homogeneous material, in other words, a simple of an appropriate size called representative volume elements(RVE). This subsection provides a brief introduction to micromechanics and homogenization in linear elasticity. It is well known that a material, e.g., cement paste, is regarded as  macro-homogeneous, but micro-heterogeneous body filling a RVE[Biot, 1955; Zaoui, 2002], which is fulfilled with the separation of scales requirement[Dormieuxet al., 2006; Salenon, 2001; Zaoui, 1997; Pichleret al., 2009]. As shown in Figure 1, the characteristic lengths  of  RVE need to be defined according to (a) to be representative, it needs to be significantly larger than characteristic dimensions , where  stands for the characteristic length of microheterogeneities within the RVE, and 










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